Bill de Blasio introduces his wife, Chirlane McCray, recently as his daughter Chiara de Blasio applauds.

New York City mayoral candidate Bill de Blasio has amassed a wide lead in the race for the Democratic nomination, coming in striking distance of winning the primary outright without the need of a widely expected runoff election, a poll released Wednesday showed.

Mr. de Blasio, the city’s public advocate, has the backing of 36% of likely Democratic voters, a 15 percentage point lead over his next closest rival, according to a new survey from the Quinnipiac University Polling Institute. City Council Speaker Christine Quinn is at 21% and former city Comptroller Bill Thompson is at 20%, vying neck-and-neck for second place.

Trailing far behind are Anthony Weiner, a former congressman, at 8%, and and John Liu, the city’s current comptroller, at 6%. According to the poll, 8% of voters in the Sept. 10 primary remain undecided.

The race, though, remains fluid. Among all Democratic likely voters, 31% say there is a “good chance” they’ll change their mind in the next 13 days.

A candidate must secure 40% of the vote to win the nomination outright; otherwise, a runoff election is to be held between the top two vote getters on Oct. 1. With nine candidates on the ballot in the Democratic primary, most political observers have considered the prospect of a runoff all but guaranteed.

If there is a runoff, according to the poll, Mr. de Blasio would clobber his competition. In a hypothetical matchup with Ms. Quinn, Mr. de Blasio leads 59% to 30%. In a potential runoff between Mr. de Blasio and Mr. Thompson, the public advocate leads 52% to 36%. And if Mr. Thompson and Ms. Quinn were to be in a runoff, he would beat her, 57% to 33%.

“Talk about breaking out of the pack,” said Maurice Carroll, director of the polling institute. “De Blasio takes a big lead into the final turn. Let’s see how he does in the home stretch.”

De Blasio’s campaign manager, Bill Hyers, released a statement saying, “Voters are responding to Bill de Blasio because he is the only Democrat who will boldly break from the Bloomberg years by raising taxes on the wealthy to invest in universal pre-K and after-school programs, ending racial profiling, and fighting to save community hospitals.”

The campaign is, indeed, heading into the home stretch. With many New Yorkers returning from summer vacations, the final push after Labor Day is expected to be intense and potentially volatile. The Democratic mayoral contenders will face off in their final televised debate – an event co-sponsored by The Wall Street Journal, NBC 4 New York, Telemundo and the city’s Campaign Finance Board – on NBC and at WSJ.com/NY at 7 p.m. Tuesday.

For Ms. Quinn, who was the early frontrunner in the race, the poll is a major setback and a clear warning that she’s in danger of not even making the runoff. Ms. Quinn aspires to be the city’s first female (and openly gay) mayor, but the poll showed Mr. de Blasio leading among women, with 30%, compared with 25% for Ms. Quinn and 21% for Mr. Thompson.

Ms. Quinn said she is not concerned about her support cratering. She said she expects there will be a runoff, that she will be in it and that ultimately her party will select her as its nominee.

“I feel incredibly positive about the position my campaign and I am in right now, heading into these final two weeks,” she said, citing three recent major newspaper endorsements. “I feel very confident about the momentum and the kind of wind we have at our back right now.”

Among likely black Democratic voters, 34% support Mr. de Blasio, compared with 25% for Mr. Thompson and 15% for Ms. Quinn. Mr. Thompson is the only black candidate in the race. Mr. de Blasio is married to a black woman, and his son, Dante, who is biracial, has played a prominent role, to wide acclaim, in the candidate’s campaign commercials.

According to the poll, Mr. de Blasio is leading among white voters, with 38%, compared with 28% for Ms. Quinn and 18% for Mr. Thompson.

When voters were asked if there’s any candidate in the Democratic primary whom they would not vote for under any circumstances, 47% said Mr. Weiner, who has been dogged by a sexting scandal. Ms. Quinn, though, came in second place in this unenviable part of the survey, with 29%, followed by Mr. Liu, at 17%. Just 6% of voters said they would not vote for Mr. de Blasio under any circumstances, and the same for Mr. Thompson.

Messrs. de Blasio and Thompson have the most enthusiastic and committed voters, the poll found. For both men, 36% of their backers say they are “very enthusiastic” and 52% said they will definitely vote for their current choice. For Ms. Quinn, 25% said they are “very enthusiastic” and 37% say they definitely will vote for her.

Nearly two-thirds of voters said the city needs to take a new direction from Mayor Michael Bloomberg, who is stepping down at year’s end, while a quarter said the city should continue in the same direction Mr. Bloomberg has been leading.

The poll of 602 likely Democratic primary voters was taken from Thursday through Tuesday and has a margin of error of plus or minus 4 percentage points.